The study of Boltzmann factors with zeros is motivated by the case of the finite-density fermion sign problem, where the practice of integrating fermions out yields precisely these sorts of singularities of the action. In [1]} it was shown that for a simplified (mean-field) model of lattice fermions in any number of space-time dimensions, perfect contours do not exist at finite chemical potential. However, neither the discussion above nor that primitive example are sufficient to rule out the existence of perfect contours for realistic lattice fermions. Whether or not such contours exist remains an important open question.
